Question

What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1?

I've narrowed it down to two but I'm not sure how to solve the middle

f(x) = 2 cos (x − π) − 1
f(x) = 2 cos πx − 1

Answer 1

This one has period 2 because

f(x) = 2 cos πx − 1 2 π/ π = 2

Answer 2

@Directrix The first 2 is the period right?

Answer 3

y = 2 cos πx − 1 The 2 in front of the cosine is the amplitude.

Answer 4

@Directrix Right, and the last number is the vertical shift, how do I solve the rest?

Answer 5

The attached visual may help.

http://www.purplemath.com/modules/grphtrig.htm

Answer 6

@Directrix Thanks, I plugged it in, so it's f(x) = 2 cos (x − π) − 1 right?

Answer 7

Look at the graph.

http://www.wolframalpha.com/input/?i=y+%3D++%3D+2+cos+%28x+%E2%88%92+%CF%80%29+%E2%88%92+1

Answer 8

Phase shift is another name for horizontal shift.

Answer 9

Look at this thread. It appears to be a discussion of your problem.

http://openstudy.com/updates/53eba266e4b01789aba451ad

@mrsteezyyy

Answer 10

f(x) = 2 cos (x − π) − 1 --> From @SithsAndGiggles

out of options

f(x) = −1 cos πx + 2

f(x) = −1 cos (x − π) + 2

f(x) = 2 cos (x − π) − 1

f(x) = 2 cos πx − 1